Method and apparatus for manufacturing objects having optimized response characteristics

ABSTRACT

A method for manufacturing an object having a potential {x} which is generated in response to a field {f} applied thereto is provided. The method includes the step of designing a geometric model of the object. A computerized mathematical model of the object is generated by discretizing the geometric model of the object into a plurality of finite elements and defining nodes at boundaries of the elements, wherein values of the field {f} and potential {x} are specified at the nodes. A material property matrix [k] is then calculated based on the relationship {f}=[k]{x}. Material property coefficients are then extracted from the material property matrix [k] for each finite element in the computerized mathematical model and the extracted material property coefficients are compared to material property coefficients for known materials to match the extracted material property coefficients to the material property coefficients for known materials. Manufacturing parameters corresponding to the matched material property coefficients are then determined. The object is then manufactured in accordance with the determined manufacturing parameters.

This is a continuation of application Ser. No. 08/994,022, filed Dec.18, 1997, now U.S. Pat. No. 6,263,252, which is a continuation ofapplication Ser. No. 08/778,270, filed Jan. 2, 1997, now U.S. Pat. No.5,796,617 which is a continuation of application Ser. No. 08/388,580,filed Feb. 14, 1995, now U.S. Pat. No. 5,594,651.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention generally relates to articles of manufacture and,more particularly, to a method and apparatus for manufacturing objectshaving response characteristics which are optimized for a desiredapplication or use.

2. Description of Related Art

An object composed of one or more materials, which is engineered andmanufactured for an intended application, must be able to withstand thestresses exerted on the object during use in the application. Forexample, a bridge, carrying a pathway or roadway over a depression orobstacle such as a body of water, must be designed to withstand thestresses created by traffic (either pedestrian or vehicle or both),temperature variations, wind, shifts in the surface of the earth whichmay be caused by earthquakes or other geological movements, etc.Similarly, aircraft components must have sufficient strength towithstand bending, sheer, torsion, and other forces placed on it.Accordingly, in a conventional engineering process, a stress analysis isperformed. The stress analysis requires a determination of the forces(or “stress-field”) which will be applied to the object during use inthe application. These stresses include, for example, thermal,mechanical, and electromagnetic forces. Knowing the stress-field enablesa determination of whether a trial design and the selected material(s)are appropriate to withstand the stresses created during use of theobject for its intended application. If a specific combination of designand material(s) is not suitable for an intended application, the objectmay be redesigned and/or new material(s) may be selected.

The above-described conventional engineering process will be discussedin greater detail with respect to FIG. 1. The initial design geometry ofthe object and the material(s) of which the object is to be composed aredefined at step 11. Geometry includes dimensions, tolerances, surfacefinish, definitions of surfaces and edges, and, in some cases, the fitbetween two mating parts. The initial design geometry may be createdusing computer-aided-design (CAD) techniques known in the art. Eachforce which will be applied to the object during intended use, and thepoints and direction of application of the respective forces, areidentified at step 12.

Stress analysis is performed at step 13. One technique for carrying outsuch a stress analysis is to create a finite-element model of the objectand utilize the finite element method to determine the suitability ofthe object for the intended application. The finite element method is anumerical analysis technique for obtaining approximate solutions to awide variety of engineering problems in which a complex part or objectis subdivided into the analyses of small simple subdivisions of the partor object. This method has been widely discussed and reference will bemade in what follows to a discussion from Huebner et al, The FiniteElement Method for Engineers, Third Edition, John Wiley and Sons, Inc.(1995). In a continuum problem, a field variable such as pressure,temperature, displacement, or stress has infinitely many values becauseit is a function of each point in the body. The finite element methodreduces the problem to one of a finite number of unknowns by dividingthe solution region into elements and by expressing the unknown fieldvariable in terms of assumed approximating functions within eachelement. The approximating functions are defined in terms of the valuesof the field variables at specified points called nodes. Nodes usuallylie on the element boundaries where adjacent elements are connected. Forthe finite element representation of a problem, the nodal values of thefield variable become the unknowns. Once these unknowns are found, theapproximating functions define the field variable throughout theassembled elements. An important feature of the finite element method isthe ability to formulate solutions for individual elements beforeputting them together to represent the entire problem. This means thatthe characteristics of each individual element may be found and then theelements may be assembled to find the characteristics of the wholestructure. The finite element method may be summarized by the followingsteps.

First, the continuum is discretized into elements. A variety of elementshapes may be used and different element shapes may be employed in thesame solution region. The number and type of elements in a given problemare generally matters of engineering judgment. For example,three-dimensional elements work best if they are either tetrahedral orhexahedral in shape. In addition, the most accurate elements have aunity aspect ratio. The next step is to assign nodes to each element andthen choose the interpolation function to represent the variation of thefield variable over the element. Once the finite element model has beenestablished, the matrix equations expressing the properties of theindividual elements may be determined. Several different approachesincluding a direct approach, a variational approach, or a weightedresidual approach may be used. The element properties are then assembledto obtain the system equations. That is, the matrix equations expressingthe behavior of the elements are combined to form the matrix equationsexpressing the behavior of the entire system. At this point, the systemequations are modified to account for any boundary conditions of theproblem. That is, known nodal values of the dependent variables or nodalloads are imposed. The resulting system of equations may then be solvedto obtain the unknown nodal values of the problem. The solution ofequations may be used to calculate other important parameters. Forexample, in a structural problem, the nodal unknowns are displacementcomponents. From these displacements, the element strains and stressesmay be calculated.

An example of the finite element method from the Huebner text will bediscussed as an aid in understanding the terminology to be used in thisspecification. FIG. 2 illustrates a linear spring system. For a typicalspring element, the relations expressing its stiffness are${\begin{bmatrix}k_{11} & {- k_{12}} \\{- k_{21}} & k_{22}\end{bmatrix}\begin{Bmatrix}\delta_{1} \\\delta_{2}\end{Bmatrix}} = \begin{Bmatrix}F_{1} \\F_{2}\end{Bmatrix}$

where k₁₁=k₁₂=k₂₁=k₂₂=k.

Under a given loading condition, each element as well as the system ofelements, must be in equilibrium. If this equilibrium condition isimposed at a particular node i,

ΣF _(i) ^((e)) =F _(i) ⁽¹⁾ +F _(i) ⁽²⁾ +F _(i) ⁽³⁾ + . . . =R _(i)  (1)

which states that the sum of all the nodal forces in one direction atnode i equals the resultant external load applied at node i. Inaccordance with conventional tensor notation, each coefficient in astiffness matrix is assigned a double subscript, e.g., ij; the number iis the subscript designating the force F_(i) produced by a unit value ofthe displacement whose subscript is j. The force F_(i) is that whichexists when δ_(j)=1 and all the other displacements are fixed. Adisplacement and a resultant force in the direction of the displacementcarry the same subscript. Thus, evaluating equation (1) at each node inthe linear spring system of FIG. 2, it can be shown that

at node 1,

k ₁₁ ⁽¹⁾ δ ₁ +k ₁₂ ⁽¹⁾δ₂ =R ₁

at node 2,

k ₂₁ ⁽¹⁾ δ ₁+(k ₂₂ ⁽¹⁾ +k ₂₂ ⁽²⁾ +k ₂₂ ⁽³⁾)δ₂+(k ₂₃ ⁽²⁾ +k ₂₃ ⁽³⁾)δ₃=0

at node 3,

(k ₃₂ ⁽²⁾ +k ₃₂ ⁽³⁾)δ₂+(k ₃₃ ⁽²⁾ +k ₃₃ ⁽³⁾ +k ₃₃ ⁽⁴⁾)δ₃ +k ₃₄ ⁽⁴⁾δ₄=0

and at node 4

k ₄₃ ⁽⁴⁾δ₃ +k ₄₄ ⁽⁴⁾δ₄ =F

Using matrix notation, these system equilibrium equations can be writtenas ${\begin{bmatrix}k_{11}^{(1)} & k_{12}^{(1)} & 0 & 0 \\k_{21}^{(1)} & \left( {k_{22}^{(1)} + k_{22}^{(2)} + k_{22}^{(3)}} \right) & \left( {k_{23}^{(2)} + k_{23}^{(3)}} \right) & 0 \\0 & \left( {k_{32}^{(2)} + k_{32}^{(3)}} \right) & \left( {k_{33}^{(2)} + k_{33}^{(3)} + k_{33}^{(4)}} \right) & k_{34}^{(4)} \\0 & 0 & k_{43}^{(4)} & k_{44}^{(4)}\end{bmatrix}\begin{Bmatrix}\delta_{1} \\\delta_{2} \\\delta_{3} \\\delta_{4}\end{Bmatrix}} = \left\{ \begin{matrix}. \\l \\0 \\F\end{matrix} \right.$

or

[k]{δ}={F}  (2)

These equations are the assembled force-displacement characteristics forthe complete system and [k] is the assembled stiffness matrix. Theseequations cannot be solved for the nodal displacements until they havebeen modified to account for the boundary conditions.

It can be seen that the stiffness matrix [k] is the sum of the followingmatrices, each matrix representing the contribution from a correspondingone of the elements: $\begin{matrix}{\left\lbrack \overset{\_}{K} \right\rbrack^{(1)} = \begin{bmatrix}k_{11}^{(1)} & k_{12}^{(1)} & 0 & 0 \\k_{21}^{(1)} & k_{22}^{(1)} & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}} & {\left\lbrack \overset{\_}{K} \right\rbrack^{(2)} = \begin{bmatrix}0 & 0 & 0 & 0 \\0 & k_{22}^{(2)} & k_{23}^{(2)} & 0 \\0 & k_{32}^{(2)} & k_{33}^{(2)} & 0 \\0 & 0 & 0 & 0\end{bmatrix}} \\{\left\lbrack \overset{\_}{K} \right\rbrack^{(3)} = \begin{bmatrix}0 & 0 & 0 & 0 \\0 & k_{22}^{(3)} & k_{23}^{(3)} & 0 \\0 & k_{32}^{(3)} & k_{33}^{(3)} & 0 \\0 & 0 & 0 & 0\end{bmatrix}} & {\left\lbrack \overset{\_}{K} \right\rbrack^{(4)} = \begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & k_{33}^{(4)} & k_{34}^{(4)} \\0 & 0 & k_{43}^{(4)} & k_{44}^{(4)}\end{bmatrix}}\end{matrix}$

Thus, it can be seen that the assembled or global stiffness matrix canbe obtained simply by adding the contribution of each element.Similarly, using boolean locating functions or other locating functions,the contribution of each element may be determined from the assembled orglobal stiffness matrix.

Thus, to perform stress analysis, the material(s) of which the object iscomposed as determined by the initial design, the forces which areapplied to the object as identified at step 12, and any constraints orboundary conditions are input into the finite element model. Since theforces {f} and the material property matrix [k] are known, the finiteelement method is used to determine the corresponding displacements {δ}using equation (2). For example, assume the forces determined at step 12are loads applied to the object. Then, since the material propertymatrix is determined by the initial choice of material(s), thedisplacement resulting from application of the loads may be determined.As noted above, these displacements may then be used to calculate thestresses and strains. The calculations for solving the matrix equationsgenerated by the finite element method are generally performed using asuitable finite element software package.

Post-processing, indicated at step 14, is carried out to determine ifthe design will perform satisfactorily. Such post-processing mayinclude, for example, a comparison of the stresses in the material tothe maximum allowable stresses dictated by the material used. If thestresses are too high, the process returns to step 11 where the part maybe made stronger by adding material, the material may be changed to onewith higher allowable stress, or a new design geometry may be utilized.If the post-processing at step 14 indicates the results are acceptable,the process proceeds to step 15 where the object is manufactured inaccordance with the design geometry and the choice of material(s)determined at step 11.

A known problem with the conventional manufacturing technique describedabove is that it uses known materials and pre-set manufacturingparameters, thereby creating a structure with fixed intrinsic(constitutive) properties. This results in over designing andinefficiency of the structure. While manufacturing processes exist thatenable the adjustment of manufacturing parameters, no method exists ofprecisely determining what the manufacturing parameters should be or thesequence in which they should be implemented so as to optimize theconstitutive properties of a particular object design. In essence, nomethod exists for determining an optimized constitutive matrix for aparticular object or for manufacturing the object in accordance withthis optimized constitutive matrix.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method for manufacturing anobject having a potential {x} which is generated in response to a field{f} applied thereto includes the step of designing a geometric model ofthe object. A computerized mathematical model of the object is generatedby discretizing the geometric model of the object into a plurality offinite elements and defining nodes at boundaries of the elements,wherein values of the field {f} and potential {x} are specified at thenodes. A material property matrix [k] is then calculated based on therelationship {f}=[k]{x}. Material property coefficients are thenextracted from the material property matrix [k] for each finite elementin the computerized mathematical model and the extracted materialproperty coefficients are compared to material property coefficients forknown materials to match the extracted material property coefficients tothe material property coefficients for known materials. Manufacturingparameters corresponding to the matched material property coefficientsare then determined. The object is then manufactured in accordance withthe determined manufacturing parameters.

In accordance with another aspect of the present invention, a method fordetermining manufacturing parameters for manufacturing an object havinga potential {x} which is generated in response to a field {f} appliedthereto includes the step of designing a geometric model of the object.A computerized mathematical model of the object is generated bydiscretizing the geometric model of the object into a plurality offinite elements and defining nodes at boundaries of the elements,wherein values of the field {f} and potential {x} are specified at thenodes. A material property matrix [k] is calculated based on therelationship {f}=[k]{x}. Material property coefficients are extractedfrom the material property matrix [k] for each finite element in thecomputerized mathematical model and the extracted material propertycoefficients are compared to material property coefficients for knownmaterials to match the extracted material property coefficients to thematerial property coefficients for known materials. Manufacturingparameters corresponding to the matched material property coefficientsare then determined.

In accordance with yet another aspect of the present invention, a methodfor determining the material properties of an object having a potential{x} which is generated in response to a field {f} applied theretoincludes the step of designing a geometric model of the object. Acomputerized mathematical model of the object is generated bydiscretizing the geometric model of the object into a plurality offinite elements and defining nodes at boundaries of the elements,wherein values of the field {f} and potential {x} are specified at thenodes. A material property matrix [k] is calculated based therelationship {f}=[k]{x}. Material property coefficients are extractedfrom the material property matrix [k] for each finite element in thecomputerized mathematical model and the extracted material propertycoefficients are compared to material property coefficients for knownmaterials to match the extracted material property coefficients to thematerial property coefficients for known materials.

In accordance with yet another aspect of the present invention, amachine for determining the manufacturing parameters of an object havinga potential {x} which is generated in response to a field {f} appliedthereto includes a designing element for designing a geometric model ofthe object. A generating element generates a computerized mathematicalmodel of the object by discretizing the geometric model of the objectinto a plurality of finite elements and defining nodes at boundaries ofthe elements, wherein values of the field {f} and the potential {x} arespecified at the nodes. A calculating element calculates a materialproperty matrix [k] based the relationship {f}=[k]{x}. An extractingelement extracts material property coefficients from the materialproperty matrix [k] for each finite element in the computerizedmathematical model. A comparing element compares the extracted materialproperty coefficients to material property coefficients for knownmaterials to match the extracted material property coefficients to thematerial property coefficients for known materials and a determiningmeans determines manufacturing parameters corresponding to the matchedmaterial property coefficients.

In accordance with yet another aspect of the present invention, amachine for determining the material properties of an object having apotential {x} which is generated in response to a field {f} appliedthereto includes a designing element for designing a geometric model ofthe object. A generating element generates a computerized mathematicalmodel of the object by discretizing the geometric model of the objectinto a plurality of finite elements and defining nodes at boundaries ofthe elements, wherein values of the field {f} and the potential {x} arespecified at the nodes. A calculating element calculates a materialproperty matrix [k] based the relationship {f}=[k]{x}. An extractingelement extracts material property coefficients from the materialproperty matrix [k] for each finite element in the computerizedmathematical model. A comparing element compares the extracted materialproperty coefficients to material property coefficients for knownmaterials to match the extracted material property coefficients to thematerial property coefficients for known materials.

These and other features and advantages of the present invention will bebetter understood from a reading of the following detailed descriptionin conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the prior art methodology for manufacturing anobject.

FIG. 2 illustrates a simple mechanical spring system for definingterminology used in this application.

FIG. 3 illustrates the methodology for manufacturing an object inaccordance with the present invention.

FIGS. 4A and 4B illustrates forces applied to the femoral head of a hipduring a one-leg stance and rising from a chair, respectively.

FIGS. 5A and 5B illustrate a force applied to an in vivo hip and theresultant stresses, respectively.

FIG. 6 illustrates a finite element model of a prosthetic hip.

FIGS. 7A and 7B illustrate material properties data bases.

FIG. 8 illustrates functional modules which may be used to implement thepresent invention.

FIG. 9 is a block diagram of an environment which may be used toimplement one or more of the functional modules of FIG. 8.

FIG. 10 is a schematic of a control computer for controlling amanufacturing machine.

DETAILED DESCRIPTION

FIG. 3 will be used to describe a methodology for manufacturing anobject or part in accordance with the present invention. As will becomeapparent from the description below, object or part (hereinafter“object”) as used herein refers to any object which may be manufacturedby a process or technique in which manufacturing parameters may becontrolled to vary constitutive or material properties within theobject. The methodology for manufacturing an object in accordance withthe instant invention is based on solutions of the equation

{f}=[k]{x}

where {f} represents a field which will be applied to the object in itsintended use, {x} represents a potential corresponding to the appliedfield, and [k] represents the material properties of the object.

The methodology of the instant invention may be utilized with anymanufacturing technique in which the manufacturing parameters may bevaried. For example, a braiding process using a braider may be used tomanufacture fiber composite objects. Fiber composite materials arefinding increasing use as the construction material for components suchas body panels of automobiles, aircraft, prosthetic implants, golf clubshafts, tennis rackets, bicycle frames, and fishing poles. Thesecomposite materials offer high strength equal to, or exceeding, that ofmetallic materials, for example, while at the same time are lighter inweight and have other improved functional properties. Parameters such asthe speed of the braider bed and/or mandrel, the thickness of thefibers, and the tension applied to the fibers are controlled to vary thestiffness properties of the fiber composite material. An example of abraider bed designed for controlled braiding of composite materials isshown in U.S. Pat. No. 4,909,127 to Skelton. Three-dimension wovenfabrics are also discussed in U.S. Pat. No. 4,975,262 to Suto.

Composite materials may also be constructed by laminating structuralfibers in appropriate matrices compatible with these fibers as describedin U.S. Pat. No. 5,023,800 to Carver et al. Fiberglass is a widely usedcomposite system which incorporates glass fibers within an epoxy resinmatrix. For formation of aircraft components, more exotic compositesystems having improved properties are desirable. Currently availablefor use are exotic inorganic materials such as carbon fibers, boronfibers, improved glass fibers, aluminum oxide fibers, inorganic whiskersof different materials and certain organic fibers such as aramides andextended chain polyethylenes. These fibers or whiskers are incorporatedas threads, fabrics, mats, or the like in appropriate resins, as forinstance thermosetting epoxies, polyesters, polyethers, polyimides, andbismaleimides or thermoplastic polyamideimines, polyether sulfones,polyether ketones, polyphenylene sulfides and other similar polymericmaterials. Composite objects may be formed utilizing moldingtechniques—using either external molds which are of a complementaryshape to an object or an internal mandrel type mold on which thecomposite object is built. A mold utilized for the formation and curingof a composite object is called a bonding tool and the curing is carriedout under precisely controlled temperatures and pressures.

A contouring press using a contouring system on a lathe or a millingmachine may be used to manufacture metal objects. Contouring refers tothe continuous removal of material in an application such asturbine-blade machining. Parameters such as the part surface, the drivesurface, and the check surface may be controlled to vary the millingtool path and thus the contouring. Part surface refers to the surface onwhich the end of the milling tool is riding; drive surface refers to thesurface against which the edge of the milling tool rides; and checksurface refers to a surface at which the current milling tool motion isto stop. Details of a contouring system are shown in Bedworth et al.,Computer-Integrated Design and Manufacturing, McGraw-Hill Inc. (1991).

Of course, the instant invention is not limited to objects formed usingbraiding, molding, or contouring, and the above discussions are merelyexamples of manufacturing techniques which may be utilized in theinventive methodology. Other processes and techniques include by way ofexample, but not by way of limitation, polymer manufacturing processes,crystallization techniques, ceramic manufacturing techniques, and thelike.

At step 21, the field(s) {f} which will be applied to the object in itsintended use, as well as the desired potential(s) or response(s) {x} tothese field(s), are defined. For example, an object may be applied witha mechanical force field, an electric current field, a magnetic field, athermal flux field, and/or a fluid velocity field. Other fields {f} maybe derived using these primary fields. For example, an acoustic fieldmay be derived by combining the mechanical force field and the fluidvelocity field. A magnetohydrodynamics field may be derived by combiningthe fluid velocity field and the magnetic field. Each of theabove-identified fields has a corresponding potential. These potentialsare displacement, corresponding to the mechanical force field; voltage,corresponding to the electric field; magnetic vector potential,corresponding to the magnetic field; temperature, corresponding to thethermal flux field; and fluid potential, corresponding to the fluidvelocity field.

As noted, the fields defined at step 21 represent one or more fieldswhich will be applied to the object in its intended use. For example, inthe case of a prosthetic hip, the field may be the mechanical forceswhich will be applied to the prosthetic hip after implant in the humanbody. For example, the arrows in FIGS. 4A and 4B represent the forces(direction and magnitude) applied to the femoral head during a one-legstance (during walking, for example) and rising from a chair,respectively. The force distributions and orientations are based on invivo studies reported at, for example, Hodge et al., “Contact Pressuresin the Human Hip Joint Measured In Vivo,” Proc. Natl. Acad. Sci. USA,83, 2879-2883 (1986). The resultant force of each of these forces wasapproximately 2000 Newtons (N), with an orientation change from one-legstance to midrise loading. As another example, in the case of a heatconduction element, the field may be the thermal flux which will beapplied to the object in its intended use. Of course, an object may beapplied with more than one field and each of these fields may be definedat step 21. For example, an electrical conductor may be applied with anelectric field, a magnetic field, and a mechanical force field in itsintended use.

The potential(s) {x} defined at step 21 define the manner in which themanufacturer desires the object to respond when the defined field orfields {f} are applied thereto. In the case of the prosthetic hip, thedefined potentials are the desired displacements (which correlatemathematically to the stresses) in the prosthetic hip when theprosthetic hip is subjected to the mechanical forces shown in FIGS. 4Aand 4B during walking and rising from a chair. If the manufacturerdesires the prosthetic hip to respond to forces in the same manner as anin vivo hip, the “desired displacements” in the prosthetic hip may, forexample, correspond to the displacements generated in an in vito hipduring walking and rising from a chair. FIG. 5A illustrates an in vivohip applied with a force of 2000 N as indicated and FIG. 5B is a tablesetting forth measures of the displacements generated at the pointslabeled A, B, C, D, E, and F in FIG. 5A in response to this appliedforce. Thus, a manufacturer desiring to manufacture a prosthetic hipwhich responds to the force indicated in FIG. 5A in the same manner asan in vivo hip would define the force {f} to be the force indicated inFIG. 5A and would define the displacements {x} to be the displacementsset forth in the table of FIG. 5B. Similarly, in the case of the heatconduction element which is applied with a thermal flux field, thedefined responses correspond to desire temperatures at various portionsof the heat conduction element when the defined thermal flux field isapplied. In the case of an electrical conductor which is applied with anelectric field, a magnetic field, and a mechanical force field, thedefined responses correspond to desired displacements at variousportions of the conductor when the defined mechanical force field isapplied, to desired magnetic vector potentials at various portions ofthe conductor when the defined magnetic field is applied, and to desiredvoltages at various portions of the conductor when the defined electricfield is applied, respectively.

At step 22, computer aided design is used to geometrically model theobject to be manufactured. Geometric modeling is a technique of usingcomputational geometry to define geometric objects. The purposes ofgeometric modeling are object representation, which mandates a completedefinition of the object for manufacturing and other applications suchas finite element analysis; design, which allows the user to input andmanipulate a geometric specification of the object; and rendering, whichuses the geometry to paint a realistic picture of the object on acomputer graphics output device. The initial geometric model of theobject or part may, for example, be based on the experience of thedesign engineer or be dictated by the intended use of the object orpart. For example, the initial geometric model of a prosthetic hip isbased on an in vivo hip. Of course, this initial geometric model may besubsequently modified for adaptation to an individual of a particularheight and/or weight. The initial design geometry of a golf club shaftis again known, i.e., a cylinder of predetermined length and diameter.Again, this initial design geometry may be modified to provide a shaftfor a golfer of a particular height or to provide a shaft having adiameter which varies, e.g., a narrower diameter near the club head.Suitable CAD software packages for carrying out this geometric modelinginclude I-DEAS (available from SDRC, Inc. of Milford, Ohio), CATIA(available from IBM of Armonk, N.Y.), and ANVIL-5000 (available fromManufacturing Consulting Services). These software packages may be run,for example, on UNIX-based work stations such as those available fromSun Microsystems or Silicon Graphics. Of course, the choice of computerwill be determined by the computational power required and the inventionis not limited in this respect. The use of such computer aided designsoftware packages permits a geometric model of an object or part to bedefined by a user and modified quickly and results in generation ofgeometry data which can be converted to formats useful in a computeraided manufacturing step and/or to formats useful a finite elementmethod step, which steps are discussed in greater detail below. It isnoted that the initial geometric model can be image data generated byscanning an object having the desired geometry. For example, the initialgeometric model in the case of a prosthetic hip can be generated byX-raying a cadaveric hip using, for example, a Siemens Somatom DR3 or aGE 9800 CT scanner. This image data may be converted to a format usableby the CAD software package or may be directly converted to a formatusable by a finite element software package (for example, a PDA-PATRAN(available from PDA Engineering) format) to be described below.

At step 23, a finite element model of the object is generated using thefinite element method. The finite element method is based on the theorythat an irregularly shaped object can be divided into smaller regularfinite elements. Each element can then be treated separately and theaggregate effect is the sum of the effects of all of the finite elementsin the object. The finite element model is created by a user using anappropriate software package which operates on the geometric modeldeveloped in step 22. Thus, the finite element software packagegenerally accesses a data file which contains the geometry of the objectdeveloped in step 21. Some integrated software packages, such as I-DEASfrom SDRC, Inc., link modules for geometric modeling and finite elementanalysis so that the user does not have to redefine the geometryspecifically for finite element analysis. Other suitable softwarepackages for generating the finite element model include MSC/NASTRAN(available from MacNeal-Schwendler Corporation), ABAQUS (available fromMacNeal-Schwendler Corporation), and ANSYS (available from SwansonManufacturing).

Thus, the finite element model is generated by dividing the geometricmodel of the object into a plurality of elements and then defining nodesat the boundaries of the elements. An exemplary finite element model fora prosthetic hip is shown in FIG. 6. A variety of element shapes may beused in the finite element model of the object. The number and types ofelements selected are generally based on the type of field and thegeometry of the object. The various finite element software packagesidentified above generally include libraries of elements and elementclusters to enable modeling of areas having particular geometries with auser-specified degree of accuracy. Thus, an element having a elementsize of a predetermined value or an element cluster of variable elementshaving a cluster size of the predetermined value may be utilized. Ifelement clusters are utilized, the cluster may be repeated throughoutthe finite element model. A cluster may include elements which havedifferent shapes. For example, if the object to be manufactured will besubject to shear forces, elements having shapes which are best suitedfor modeling shear forces may be utilized and oriented as appropriate.When these elements are grouped together, they may define a clusterwhich may be repeated, for example, in areas having similar geometriesand/or which are applied with similar forces. In addition, differentsize elements may be used to model object portions of criticaltolerance. So-called super-elements may be used where tolerance is notcritical. Since the methodology of the invention is typically aniterative process as will be discussed below, if, for example, it isdetermined in a first iteration that there are one or more portions ofthe object where the nodal values do not change much, for computationalpurposes, a second later iteration may generate a finite element modelof the object which includes one or more super-elements in these areasin order to simplify subsequent calculations.

The finite element model is completed by specifying the values and/ordirections of the above-described fields {f} and potentials {x} at thenodes of the discretized object. In addition, any appropriate boundaryconditions are imposed.

At step 24, the finite element software package is programmed to solvefor the material property matrix [k] using the relationship {f}=[k]{x}.That is,

[k]{x}={f}

[k]{x}{x} ⁻¹ ={x} ⁻¹ {f}

[k]={x} ⁻¹ {f}

Since the field {f} and the potential {x} have been defined at step 21,the material property matrix [k] may be calculated. When {f} is themechanical force field and {x} is the displacement, [k] is the stiffnessmatrix. When {f} is the thermal flux field and {x} is the temperature,[k] is the thermal conductivity. When {f} is the magnetic field and {x}is the magnetic vector potential, [k] is the magnetic reluctivity. When{f} is an electric current field and {x} is the voltage, [k] iselectrical conductivity. The calculation of the matrix [k] at step 24when the fields and potentials have been defined as described at steps21 determines the optimum or near-optimum material property matrix forpermitting a manufacturer to manufacture an object having desiredresponses for a specific application, i.e., for a specific applicationof forces.

At step 25, the finite element software package is used to extract thematerial property coefficients for each of the elements in the finiteelement model from the material property matrix [k]. Specifically, thematerial property matrix [k] which is calculated at step 24 is theglobal or assembled material property matrix [k]. As previouslydiscussed, the material property coefficients for a particular elementof the finite element model may be extracted from such a global orassembled matrix using a boolean locating function or some otherlocating function. For example, with reference to FIG. 6, the materialproperty coefficients for element 601 are extracted, followed by thematerial property coefficients for element 602, etc. This procedure isrepeated for each element in the model in order to generate a datasequence representing the material properties of the prosthetic hip atsmall volume increments.

At step 26, the extracted material property coefficients are comparedwith known material property coefficients in a material property database or data bases. FIG. 7A illustrates one organization of a materialproperty data base 700. Material property data base 700 characterizes aplurality of materials M1-1, M1-2, . . . , M1-n by the values ofstiffness properties such as Young's modulus (E) and Poisson's ratio(σ). For example, material M1-1 may be aluminum having a Young's modulusof 7.2×10¹⁰ Pa and a Poisson's ratio of 0.32. Material M1-2 may bealuminum having a Young's modulus of 6.9×10¹⁰ Pa and a Poisson's ratioof 0.35. Material M1-n may be cast iron having a Young's modulus of8.8×10¹⁰ Pa and a Poisson's ratio of 0.30. Of course, the invention isnot limited to these specific materials. Respectively associated witheach of these materials M1-1, M1-2, . . . , M1-n are a manufacturingprocess and the specific parameters of that process (such astemperature, pressure, etc.) which will produce the material with thecorresponding stiffness properties. Similarly, as shown with referenceto FIG. 7B, a material property data base 701 may characterize aplurality of materials M2-1, M2-2, . . . , M2-n by the values ofelectrical conductivity (σ′). Again, respectively associated with eachof these materials M2-1, . . . , M2-n are a manufacturing process andthe specific parameters of that process which will produce the materialwith the corresponding electrical conductivity. Similar material databases may be used to characterize materials by their thermalconductivity or magnetic reluctivity and to identify the manufacturingmethod and manufacturing parameters associated with each material.

Thus, the material property data bases are archives of material propertycoefficients with their corresponding manufacturing process andmanufacturing-process control parameters. Such data bases are createdand maintained by industrial manufacturers, government agencies, andresearch institutes. For example, when a material such as a metal, aplastic, or a composite is created using a particular manufacturingprocess, its properties may be determined through standard testingmethods such as ASTM testing methods. When these properties have beendetermined, the set of manufacturing parameters such as temperature,pressure, etc. which was used to create the material having theseproperties is correlated to the material in order that the material maybe reproduced in the future.

The comparison at step 26 between the extracted material propertycoefficients and the material properties data base is used to determinewhich material in the data base has material properties which match ormost closely match the properties corresponding to the extractedmaterial property coefficients. Thus, referring to FIG. 6, thecomparison will result in the identification of a first set ofmanufacturing parameters which will produce the portion of theprosthetic hip corresponding to element 601 with the desired stiffnessproperties; the identification of a second set of manufacturingparameters which will produce the portion of the prosthetic hipcorresponding to element 602; etc. The above-described comparisons maybe carried out, for example, using a knowledge base having a fact basefor storing the extracted material property coefficient data for each ofthe elements (e.g., elements 601, 602, etc. of FIG. 6) and the materialproperty data from the material data base, and a rule base containingrules for comparing and matching the extracted material property datafor each of the elements and the material property data from thematerial data base. The level of matching (e.g., a perfect match, aclose match) is application specific and is related, inter alia, to howmuch tolerance is permitted. If the object to be manufactured is acritical component, a very close or perfect match is desirable. If theobject to be manufactured is a non-critical component, the matchingcriteria may be relaxed. Other criteria such as cost and the availablemanufacturing equipment may also determine the level of matching. Thus,by performing step 26, the sets of manufacturing-process controlparameters for each and every portion of object are determined.

At step 27, the determined sets of manufacturing-process controlparameters are ordered or sequenced to define the manufacturing-processcontrols which are necessary to manufacture the object. Themanufacturing control parameters may be used to implement numericalcontrol of the manufacturing equipment used to manufacture the object.Numerical control refers to the use of coded numerical information inthe automatic control of manufacturing equipment. For machine tools,this might refer to the motion of the cutting tool or the movement ofthe part being formed against a rotating tool. The process of layingcomposite material to form lightweight alternatives to machined metalparts may also be implemented using numerical control. The necessarygeometry and motion statements for manufacturing the object may then beprogrammed using a general purpose numerical control language to developmanufacturing control data. One such language is APT-AC NumericalControl Processor Program (available from IBM Corporation, Armonk,N.Y.). The APT-AC processor is a computer application program thataccepts as input user-oriented language statements that describe thenumerical control operations to be performed. A postprocessor mayfurther process the manufacturing control data to tailor the informationto a specific manufacturing process. At step 28, the postprocessed datais supplied to a computerized manufacturing device which uses thesupplied data to control the manufacturing of the object. The datasupplied to the computerized manufacturing device controls themanufacturing device to synthesize the object, which object has thedesired specifically calculated material properties. For example, assumethe manufacturing is carried out using a braider for manufacturing acomposite material. During the weaving of the composite, by allowing thecomputer to control the speed of various machine parts, the tightness ofthe weave is controlled. The tighter the weave, the higher the stiffness(low flexibility). For example, in the case of the prosthetic hip,regions of both high and low stiffness are required. Using the geometricmodel and the extracted material property coefficients, themanufacturing process and specifically, the tightness of the weave, canbe controlled to provide a region of high stiffness (e.g., the regiondefined by element 601 in FIG. 6) and a region of low stiffness (e.g.,the region defined by element 603 in FIG. 6). By appropriatelycontrolling the manufacturing process in accordance the inventivemethodology, a prosthetic hip may be produced which responds to appliedloads in a manner which is substantially identical to manner in whichthe human hip would respond to the same applied load. Such a prosthesiscan be developed with specific response characteristics for a particularindividual.

The above-described methodology is typically carried out as an iterativeprocess. For example, the results of an initial iteration may generallyindicate that a fiber composite manufactured using a braider providesthe best match to the extracted material property coefficients in theintended application. Thus, in a second subsequent iteration, the finiteelement model may be modified to take into account the smallestincremental volume that can be controllably braided using acomputer-controlled braider. Preferably, each of the elements in thefinite element model corresponds to no less than the smallestincremental volume that can be controllably manufactured using themanufacturing technique by which the object is to be manufactured. Forexample, for a braiding process using a braider, the smallest volumethat can be controllably braided is approximately one cubic millimeter.In other words, it is possible to controllably vary a braid pattern toproduce an object having material or constitutive properties which varyon the order of a cubic millimeter. This smallest incremental volumewill of course vary in accordance with the manufacturing process ortechnique selected and may, in addition, be dependent on availablemanufacturing equipment. Thus, although the smallest incremental volumethat can be braided by a state-of-the-art braider is one cubicmillimeter, it is not necessarily true that all braiders will be capableof such operation. Accordingly, in such cases, the smallest incrementalvolume is determined by the capabilities of an available braider. Itwill be appreciated that as manufacturing techniques improve and smallerincremental volumes can be controllably manufactured, the methodology ofthe instant invention may be utilized with resized or different shapedelements.

The mathematics of the inventive method are valid for other types ofmanufacturing processes other than composites such as the manufacturingof metals, plastics, and ceramics. The inventive method is also validfor manufacturing objects based on their desired responses to heat andelectric currents. In short, the inventive method can be used for anycomputer controlled manufacturing process, where precisionvolumetrically controlled manufacturing is desired.

The method of the present invention is particularly useful whenincreased efficiency of an object is desired. In traditionalmanufacturing, the emphasis is on precision manufacturing of an object'sgeometry, without much, if any, control over the internal structuralmakeup of this geometry. In accordance with inventive methodology, thematerial matrix is the unknown and an iterative process may be carriedout to optimize the material property matrix while keeping the geometryfixed.

Thus, in accordance with the present invention, the input parameters ofany process may be precisely varied to create an object with a preciselydefined material property matrix. As manufacturing continues to improve,the above-described methodology is applicable even though the smallestincremental volume that can be controllably manufactured may continue todecrease in size.

FIG. 8 illustrates various functional modules which may be used toimplement the methodology of the instant invention. Acomputer-aided-design (CAD) module 801 is a three-dimensional graphicssoftware program for generating an geometrical model definition. Such ageometrical model definition includes coordinate points preciselylocating the object design in a three-dimensional coordinate system.This may be provided by a graphics software package using, for example,X, Y, and Z coordinate points and appropriate locating vectors wherenecessary. The three-dimensional graphics software package utilizesappropriate data structures for defining particular points in the database of the graphics program. By utilizing algorithms in the graphicsprogram, other points in the object can be defined and generated. Thegraphics program preferably utilizes appropriate vector and matrixroutines whereby an object can be rotated or otherwise moved in computermemory and can be dimensioned whereby the coordinates for any one pointare known with respect to other points. As noted above, suitable CADsoftware packages include I-DEAS (available from SDRC, Inc. of Milford,Ohio), CATIA (available from IBM), and ANVIL 5000 (available fromManufacturing Consulting Services).

A finite element module 802 is used to generate the finite element modelof the object from data stored in the graphics program data base. Finiteelement module 802 is a software package for dividing the objectdesigned using computer-aided-design module 801 into a plurality ofelements and expressing one or more unknown field variables in terms ofassumed approximating functions within each element. Finite elementmodule 802 is programmed to calculate the optimum material propertiesfor each element as discussed above. Suitable software packages forfinite element module 802 include MSC/NASTRAN (available fromMacNeal-Schwendler Corporation), ABAQUS (available fromMacNeal-Schwendler Corporation), and ANSYS (available from SwansonManufacturing).

A materials data base module 803 is an archive or archives of materialproperty coefficients with their corresponding manufacturing process andmanufacturing-process control parameters. The archives thus correlatethe properties of materials to the manufacturing process andmanufacturing process parameters used to create the materials.

A comparison module 804 compares the material properties determinedusing finite element module 802 to the material data in material database module 803 in order to determine (1) which material has materialproperties which match or most closely match the material propertiesdetermined using finite element module 802 and (2) the manufacturingprocess and manufacturing process parameters associated with thismatched material. Comparison module 804 may be implemented, for example,by a knowledge base having a fact base for storing material propertydata from finite element module 802 and material property data frommaterial data base module 803 and a rule base containing rules forcomparing and matching the material property data from finite elementmodule 802 and the material property data from material data base module803.

A manufacturing module 805 translates and sequences the manufacturingparameters derived from comparison module 804 to provide manufacturinginstructions to a manufacturing machine for manufacturing an object inhaving the geometry defined using computer-aided-design module 801. Themanufacturing of the object may be carried out by a machine suitable forthe particular material. For example, metals may be manufactured byreproducing surface geometry (surface points in space), composites maybe manufactured by controlling weave configuration and fiber choice, andpolymers may be manufactured by chemical choice, temperature, andpressure. Computer assistance in manufacturing allows machines to bequickly adjusted to vary the manufacturing process from one object tothe next or within various regions of a single object.

FIG. 9 is a block diagram of the configuration of an environment 900which may be used to implement the various functional modules describedabove. Examples of this environment include (but are not limited to)IBM-PC compatible personal computers and UNIX-based workstations such asthose available from Sun Microsystems or Silicon Graphics. It should beunderstood that the environment of the instant invention is not limitedto any type or brand of computer, and thus contemplates microcomputersto supercomputers. In addition, while FIG. 9 illustrates the details ofa single environment, the modules of FIG. 8 may be implemented on morethan one environment. For example, a first environment may be used toimplement CAD module 801 while a second different environment may beused to implement finite element module 802. Information may beexchanged between environments using floppy disks or using standardcommunication packages. Alternatively, a single environment may be usedto implement both CAD module 801 and finite element module 802.Environment 900 includes a central processing unit (CPU) 901 such as aRISC-based or an IBM PC-compatible CPU which is plugged into bus 903.One or more of the modules of FIG. 8 are loaded in memory 905 duringoperation. Input is received via an I/O device 907, after which theinput passes through a buffer 909 and then to memory 905 via bus 903. Itshould be understood that the I/O device can be any standard inputdevice, such as a disk, tape, keyboard, mouse, touch screen, or anycompatible or equivalent means for manually or automatically enteringinformation or commands. In order for a user to observe the results asinformation is entered into the present invention and as progress ismade, a preferred embodiment also contemplates the use of a visualdisplay device 911 as an example of an output devices. Other outputdevices could include printers, magnetic or optical disks, tape, etc. AROM 913 may store programs for the overall control of environment 900.

FIG. 10 is a control computer schematic for a generalized controlcomputer using a control computer 950. The control computer isdownloaded with the manufacturing instructions generated bymanufacturing module 805 of FIG. 8. Information such as braider bedspeed, fiber tension, temperature, pressure, etc. is obtained fromsensors 952 of a manufacturing machine in digital format (on/off,open/closed) or analog format (voltage). Analog inputs are converted toa digital representation by analog-to-digital converter 953 of controlcomputer 950. Control computer 950 includes a processor 960 foranalyzing the information from sensors 952 and generating signals whichare supplied to actuators 954 for adjusting the settings of themanufacturing machine in accordance with the downloaded manufacturinginstructions. In addition to analog and digital outputs, pulse outputsmay be provided to drive stepping motors, frequently used with machinetools and other equipment. Of course, the specifics of control computer950 will depend on the manufacturing machine which is utilized. Detailsof control computers useful in specific manufacturing processes may befound, for example, in the above-identified Bedworth text.

The following examples are provided to illustrate applications of themethodology of the instant invention.

EXAMPLE I

The manufacturing of a composite fiber golf club shaft in accordancewith the present invention will be described. In the case of the golfclub shaft, the governing equation is

{f}=[k]{x}

A finite element model of the golf club shaft is created. Golf clubmanufacturers maintain data bases which specify the forces {f} a shaftis subjected to (torsion, compression, tension, etc.) for different clubhead speeds. These forces are used to define the forces at the nodes ofthe finite element model.

A golfer generally desires a golf club shaft to respond in a particularway to these various forces. For example, a golf professional generallywants the shafts for a pitching wedge, nine-iron, and eight-iron to havea flex point (i.e., a point of relatively low stiffness) near the clubhead; the shafts for a seven-iron, a six-iron, and a five-iron to have aflex point near midshaft; the shafts for a four-iron, a three-iron, anda two-iron to have a flex point just above midshaft; and the shaft for adriver to have a flex point just below the grip. In each of these fourcases, the shaft thus has a unique set of desired deflections {x}. Thesedesired deflections {x} thus define the displacements at the nodes ofthe finite element model. Accordingly, four different finite elementanalyses are carried out.

Since the forces and the displacements of the finite element model havebeen defined, the global stiffness matrices for each of the four casesmay be calculated. Using boolean locating functions, the stiffnesscoefficients for the individual elements are determined. Thesedetermined stiffness coefficients are matched with stiffnesscoefficients from industrial databases. The manufacturing parameterscorresponding to the matched coefficients are appropriately translatedand sequenced to generate manufacturing instructions. Thesemanufacturing instructions are then supplied to a composite weavingmachine and the braider bed speed and the fiber tension areappropriately controlled to produce the golf shafts. For example, if itis determined that a carbon fiber provides the best match to thedetermined stiffness coefficients, a carbon fiber is placed on anappropriate weaving machine. As the weaving is performed, the speed ofthe braider bed and the tension on the fibers is varied in accordancewith the generated manufacturing instructions so that certain portionsof the golf club shaft will have a tight weave and other portions willhave a looser weave. Portions of the shaft having the tighter weave willbe stiffer than portions with the loose weave.

EXAMPLE II

The manufacturing of a carbon fiber filled composite hip replacement inaccordance with the present invention will be described. In the case ofa composite hip replacement, the governing equation is once again

{f}=[k]{x}

First, a finite element model of the normal bone geometry (both corticaland cancellous layers) is created. The stiffness properties of eachlayer are then defined. These stiffness properties are a function ofYoung's modulus and Poisson's ratio. These stiffness properties are usedto define the stiffness at the nodes of the finite element model. Next,the loads of walking, rising from a chair, climbing stairs, etc. aredefined. These loads are used to define the forces at the nodes of thefinite element model. These stiffness properties and loads are knownquantities which have been published in numerous journals, e.g., Hodgeet al., Contact Pressures in the Human Hip Joint Measured In Vivo, Proc.Natl. Acad. Sci. USA, 83 2879-2883 (1986); Fung, Biomechanics,Mechanical Properties of Human Tissue, Springer-Verlag, N.Y. (1981).

Since the forces {f} and the stiffness [k] of the finite element modelhave been defined, the displacements {x} (which are mathematicallyrelated to the stress) may be determined. Using boolean locatingfunctions, the resulting matrix data is analyzed to determine the stressat the elements of the finite element model.

Since the stress {x} at the elements of the finite element model hasbeen determined, it may now be treated as a known quantity andrepresents the ideal stress distribution that it is desired to achievein the composite hip replacement. Thus, the material stiffness matrix[k] may now be treated as an unknown.

A finite element model is again created, but now includes another layer,namely, the artificial hip embedded in the cancellous bone area. Forexample, as discussed in St. Ville et al., “The Anatomy of Midthigh PainAfter Total Hip Arthroplasty”, a finite element analysis may beperformed using the fine mesh model of FIG. 6 which includes 5207 nodesand 5040 isoparametric solid elements. Both hexahedronal andpentahedronal elements are used in the mesh of FIG. 6 to ensure accurateshape adherence. The previously calculated displacement data {x} definesthe displacement at each node of the finite element model.

The loads it is desired to subject the composite hip replacement to aredefined. Thus, loads such as walking, one leg stance, etc. are used. Thechoice of loads depends on the nature of the composite hip replacementbeing designed. These loads are generally known quantities as notedabove, for example, with respect to Hodge et al., “Contact Pressures inthe Human Hip Joint Measured In Vivo,” Proc. Natl. Acad. Sci. USA, 83,2879-2883 (1986). These loads define the forces {f} at the nodes of thefinite element model.

Since the displacement {x} and forces {f} at the nodes of the finiteelement model have been defined, the global stiffness matrix [k] may becalculated. Using boolean locating functions or other types of locatingfunctions, the stiffness coefficients at each of the nodes aredetermined. Iterative optimization techniques may be used to calculatethe ideal stiffness properties at the elements of the finite elementmodel.

These determined stiffness coefficients are matched with stiffnesscoefficients from a material property data base. The manufacturingparameters corresponding to the matched coefficients are appropriatelytranslated and sequenced to generate manufacturing instructions. Thesemanufacturing instructions are then supplied to a composite weavingmachine and the braider speed and the fiber tension are appropriatelycontrolled to produce the composite hip replacement.

Of course, it should be understood that the present inventioncontemplates other configurations of modules, and it is not limited tothe specific implementation noted above.

Any application, patent, technical document, textbook, or otherpublication cited herein should be construed to be incorporated byreference as to any subject matter deemed essential to the presentdisclosure.

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample, and not limitation. Thus, the breadth and scope of the presentinvention should not be limited by any of the above-described exemplaryembodiments, but should be defined only in accordance with the followingclaims and their equivalents.

I claim:
 1. A method for manufacturing an object having a potential {x}that is generated in response to a field {f} applied thereto, the methodcomprising: (a) generating a computerized mathematical model of theobject by discretizing a geometric model of the object into a pluralityof finite elements and specifying values for the field {f} and potential{x} relative to the finite elements; (b) calculating a material propertymatrix [k] based on the relationship {f}=[k]{x}; (c) extracting materialproperty coefficients from the material property matrix [k] for eachfinite element in the computerized mathematical model; (d) comparing theextracted material property coefficients to material propertycoefficients for known materials to match the extracted materialproperty coefficients to the material property coefficients for knownmaterials; (e) determining at least one material for the object and amanufacturing process for manufacturing the material based on thematched material property coefficients; (f) modifying the computerizedmathematical model of the object based on the determined material andmanufacturing process; (g) repeating (b) through (d) based on themodified computerized mathematical model; (h) determining manufacturingparameters for manufacturing the object based on the matched materialproperty coefficients obtained by the repeating of (b) through (d); and(i) controlling manufacturing equipment in accordance with themanufacturing parameters determined in (h) to thereby manufacture theobject.
 2. The method according to claim 1, wherein the computerizedmathematical model is modified based on a smallest volume incrementwhich can be manufactured using the manufacturing process determined at(e).
 3. The method according to claim 1, wherein the field {f} is amechanical force field and the potential {x} is a displacement.
 4. Themethod according to claim 1, wherein the field {f} is an electriccurrent field and the potential {x} is a voltage.
 5. The methodaccording to claim 1, wherein the field {f} is a magnetic field and thepotential {x} is a magnetic vector potential.
 6. The method according toclaim 1, wherein the field {f} is a thermal flux field and the potential{x} is a temperature.
 7. The method according to claim 1, wherein thefield {f} is a fluid velocity field and the potential {x} is a fluidpotential.
 8. The method according to claim 1, wherein the controllingof the manufacturing equipment comprises controlling a braider.
 9. Themethod according to claim 8, wherein the controlling of themanufacturing equipment comprises controlling tensions applied to fibersused in the braider.
 10. The method according to claim 8, wherein thecontrolling of the manufacturing equipment comprises controlling a speedof one or both of a braider bed and mandrel of the braider.
 11. Themethod according to claim 8, wherein the controlling of themanufacturing equipment comprises controlling a thickness of fibers usedin the braider.
 12. The method according to claim 1, wherein thecontrolling of the manufacturing equipment comprises controlling abonding tool.
 13. The method according to claim 12, wherein thecontrolling of the manufacturing equipment comprises controllingtemperatures and pressures of the bonding tool.
 14. The method accordingto claim 1, wherein the controlling of the manufacturing equipmentcomprises controlling the incorporation of fibers in resins.
 15. Themethod according to claim 1, wherein the object being manufactured is aprosthetic implant for replacing a body part and force {f} anddisplacement {x} are specified based on in vivo forces applied to thebody part to be replaced and the in vivo displacements generated in thebody part to be replaced when the forces are applied thereto.
 16. Anobject made in accordance with the method of claim 1, wherein the objectis selected from the group consisting of an automobile part, an aircraftpart, a prosthetic implant, a golf club shaft, a tennis racket, abicycle frame, and a fishing pole, and wherein different portions of theobject have different material properties corresponding to the matchedmaterial property coefficients.
 17. A method for determining machinecontrol instructions for manufacturing an object having a potential {x}that is generated in response to a field {f} applied thereto, the methodcomprising: (a) generating a computerized mathematical model of theobject by discretizing a geometric model of the object into a pluralityof finite elements and specifying values of the field {f} and potential{x} relative to the finite elements; (b) calculating a material propertymatrix [k] based on the relationship {f}=[k]{x}; (c) extracting materialproperty coefficients from the material property matrix [k] for eachfinite element in the computerized mathematical model; (d) comparing theextracted material property coefficients to material propertycoefficients for known materials to match the extracted materialproperty coefficients to the material property coefficients for knownmaterials; (e) determining at least one material for the object and amanufacturing process for manufacturing the material based on thematched material property coefficients; (f) modifying the computerizedmathematical model of the object based on the determined material andmanufacturing process; (g) repeating (b) through (d) based on themodified computerized mathematical model; (h) determining manufacturingparameters for manufacturing the object based on the matched materialproperty coefficients obtained by the repeating of (b) through (d); and(i) generating machine control instructions for controllingmanufacturing equipment in accordance with the manufacturing parametersdetermined at (h).
 18. The method according to claim 17, wherein thecomputerized mathematical model is modified based on a smallest volumeincrement which can be manufactured using the manufacturing processdetermined at (e).
 19. The method according to claim 17, wherein theobject being manufactured is a prosthetic implant for replacing a bodypart and force {f} and displacement {x} are specified based on in vivoforces applied to the body part to be replaced and the in vivodisplacements generated in the body part to be replaced when the forcesare applied thereto.
 20. The method according to claim 17, wherein thegenerating of machine control instructions comprises generating machinecontrol instructions for controlling a braider.
 21. The method accordingto claim 20, wherein the generating of machine control instructionscomprises generating machine control instructions for controllingtensions applied to fibers used in the braider.
 22. The method accordingto claim 20, wherein the generating of machine control instructionscomprises generating machine control instructions for controlling aspeed of one or both of a braider bed and a mandrel of the braider. 23.The method according to claim 20, wherein the generating of machinecontrol instructions comprises generating machine control instructionsfor controlling a thickness of fibers used in the braider.
 24. Themethod according to claim 17, wherein the generating of machine controlinstructions comprises generating machine control instructions forcontrolling a bonding tool.
 25. The method according to claim 24,wherein the generating of machine control instructions comprisesgenerating machine control instructions for controlling temperatures andpressures of the bonding tool.
 26. The method according to claim 17,wherein the generating of machine control instructions comprisesgenerating machine control instructions for controlling theincorporation of fibers in resins.
 27. A computer system programmed toperform the method of claim
 17. 28. A control system programmed withmachine control instructions for controlling manufacturing equipment tomanufacture an object, wherein the machine control instructions aregenerated in accordance with the method of claim
 17. 29. Manufacturingequipment comprising a control system programmed with machine controlinstructions for controlling manufacturing equipment to manufacture anobject, wherein the machine control instructions are generated inaccordance with the method of claim
 17. 30. The manufacturing equipmentaccording to claim 29, wherein the manufacturing equipment comprises abraider.
 31. The manufacturing equipment according to claim 29, whereinthe manufacturing equipment comprises a bonding tool.
 32. Themanufacturing equipment according to claim 29, wherein the manufacturingequipment incorporates fibers into resins.